import time
from typing import Tuple, Dict, Union, List
import tensorflow as tf
import matplotlib.pyplot as plt
import matplotlib.cm as cm
import numpy as np
from sklearn.manifold import TSNE
from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_samples, silhouette_score
NUMBER_PARAM = 10
REGULARIZER_TYPE = 'kernel_regularizer'
LS_KERNEL_REGULARIZER = np.linspace(0, 1e-4, NUMBER_PARAM)
LS_ACTIVITY_REGULARIZER = np.zeros(NUMBER_PARAM)
(x_train, y_train), (x_test, y_test) = tf.keras.datasets.mnist.load_data()
x_train_norm = x_train/np.max(x_train)
x_test_norm = x_test/np.max(x_test)
The following model is to minimize loss function, $L_T$, in terms of loss from regular autoencoder, $L$, plus regularization term, $R$.
Encoding layer:
$h = \alpha_e(W_1 \times\ x + b_1)$, where $\alpha_e(.)$ is activation function ReLU,
and the number of hidden units in $h$ is 196. Hence $h$ is a 196x1 vector in 196-dim latent space, $W_1$ is 196x748 weight matrix and $b_1$ is the bias term in the form of 196x1 vector.
Decoding layer:
$x' = \alpha_d(W_2 \times\ h + b_2)$, where $\alpha_d(.)$ is activation function sigmoid, $x'$ is the output of the autoencoder
which is optimized to reconstruct back to input $x$.
Loss function:
$L_T = L + R = ||x - x'||^2 + \lambda_a\sum |h_i| + \lambda_k\sum |W_1|$, where $i$ is the number of hidden units, $\lambda_k\ $and $\lambda_a\ $are kernel and activity regularizer respectively, l1 regularization is used.
class Autoencoder(tf.keras.Model):
def __init__(
self,
input_shape: Tuple[int,int],
encoding_dim: int,
activity_regularizer: float,
kernel_regularizer: float,
**kwargs
) -> None:
super().__init__(**kwargs)
self.encoding_dim = encoding_dim
self.encoder = tf.keras.Sequential([
tf.keras.layers.Flatten(),
tf.keras.layers.Dense(
encoding_dim,
activation='relu',
activity_regularizer=tf.keras.regularizers.L1(activity_regularizer),
kernel_regularizer=tf.keras.regularizers.L1(kernel_regularizer)
)
])
self.decoder = tf.keras.Sequential([
tf.keras.layers.Dense(
input_shape[0]*input_shape[1],
activation='sigmoid'
),
tf.keras.layers.Reshape(input_shape)
])
def call(self, inputs):
encoded = self.encoder(inputs)
decoded = self.decoder(encoded)
return decoded
def training(
train_set: np.ndarray,
test_set: np.ndarray,
activity_regularizer: float,
kernel_regularizer: float,
encoding_dim: int,
) -> Dict[str, Union[Autoencoder, float, int, np.ndarray]]:
# build
autoencoder = Autoencoder(
input_shape=(28, 28),
encoding_dim=encoding_dim,
activity_regularizer=activity_regularizer,
kernel_regularizer=kernel_regularizer,
)
autoencoder.compile(optimizer='adam', loss='mse')
callback = tf.keras.callbacks.EarlyStopping(monitor='val_loss', patience=3, min_delta=0.0001)
# fit
print(f'Training start:')
print(f'activity_regularizer = {activity_regularizer}')
print(f'kernel_regularizer = {kernel_regularizer}')
start = time.time()
history = autoencoder.fit(
train_set, train_set,
callbacks=[callback],
epochs=100,
batch_size=256,
shuffle=True,
verbose=0,
validation_data=(test_set, test_set)
)
end = time.time()
# eval
training_loss = history.history.get('loss')[-1]
testing_loss = history.history.get('val_loss')[-1]
epoch = max(history.epoch)
print('Training results:')
print(f'training_loss = {training_loss}')
print(f'testing_loss = {testing_loss}')
print(f'epoch = {epoch}')
print(f'time passed = {int(round(end-start))}s')
print('-'*100)
# return
w1, _, _, _ = autoencoder.get_weights()
w1_reshape = w1.T.reshape((encoding_dim,28,28))
result = {
'hyperparam': {
'activity_regularizer': activity_regularizer,
'kernel_regularizer': kernel_regularizer,
},
'results': {
'training_loss': training_loss,
'testing_loss': testing_loss,
'epoch': epoch,
'model': autoencoder,
'w1_reshape': w1_reshape,
}
}
return result
training_results = list()
for kernel_regularizer, activity_regularizer in zip(LS_KERNEL_REGULARIZER,LS_ACTIVITY_REGULARIZER):
result = training(
train_set=x_train_norm,
test_set=x_test_norm,
activity_regularizer=activity_regularizer,
kernel_regularizer=kernel_regularizer,
encoding_dim=196
)
training_results.append(result)
Training start: activity_regularizer = 0.0 kernel_regularizer = 0.0 Training results: training_loss = 0.001473878393881023 testing_loss = 0.0014665934722870588 epoch = 21 time passed = 30s ---------------------------------------------------------------------------------------------------- Training start: activity_regularizer = 0.0 kernel_regularizer = 1.1111111111111112e-05 Training results: training_loss = 0.005007409490644932 testing_loss = 0.004947695415467024 epoch = 55 time passed = 72s ---------------------------------------------------------------------------------------------------- Training start: activity_regularizer = 0.0 kernel_regularizer = 2.2222222222222223e-05 Training results: training_loss = 0.007151870522648096 testing_loss = 0.007050069980323315 epoch = 55 time passed = 71s ---------------------------------------------------------------------------------------------------- Training start: activity_regularizer = 0.0 kernel_regularizer = 3.3333333333333335e-05 Training results: training_loss = 0.008163469843566418 testing_loss = 0.008001532405614853 epoch = 72 time passed = 91s ---------------------------------------------------------------------------------------------------- Training start: activity_regularizer = 0.0 kernel_regularizer = 4.4444444444444447e-05 Training results: training_loss = 0.00946621410548687 testing_loss = 0.00927070714533329 epoch = 68 time passed = 86s ---------------------------------------------------------------------------------------------------- Training start: activity_regularizer = 0.0 kernel_regularizer = 5.555555555555556e-05 Training results: training_loss = 0.010429237969219685 testing_loss = 0.010227708145976067 epoch = 77 time passed = 98s ---------------------------------------------------------------------------------------------------- Training start: activity_regularizer = 0.0 kernel_regularizer = 6.666666666666667e-05 Training results: training_loss = 0.011244737543165684 testing_loss = 0.011030125431716442 epoch = 65 time passed = 80s ---------------------------------------------------------------------------------------------------- Training start: activity_regularizer = 0.0 kernel_regularizer = 7.777777777777778e-05 Training results: training_loss = 0.012330700643360615 testing_loss = 0.012090915814042091 epoch = 72 time passed = 88s ---------------------------------------------------------------------------------------------------- Training start: activity_regularizer = 0.0 kernel_regularizer = 8.888888888888889e-05 Training results: training_loss = 0.013071522116661072 testing_loss = 0.01280683558434248 epoch = 75 time passed = 92s ---------------------------------------------------------------------------------------------------- Training start: activity_regularizer = 0.0 kernel_regularizer = 0.0001 Training results: training_loss = 0.014319300651550293 testing_loss = 0.014037657529115677 epoch = 75 time passed = 92s ----------------------------------------------------------------------------------------------------
MSE loss ($L_T$) against hyperparameter, kernel_regularizer ($\lambda_k$), for training set and testing set
def loss_plot(results) -> None:
param = list()
training_loss = list()
testing_loss = list()
for result in results:
param.append(result['hyperparam'][REGULARIZER_TYPE])
training_loss.append(result['results']['training_loss'])
testing_loss.append(result['results']['testing_loss'])
plt.figure(figsize=(12, 8))
plt.plot(param, testing_loss, 'bs', label='testing_loss')
plt.plot(param, training_loss, 'r^', label='training_loss')
plt.ylabel('loss')
plt.xlabel(REGULARIZER_TYPE)
plt.title('Training loss vs testing loss')
plt.legend(loc='upper left')
plt.show()
plt.close()
loss_plot(results=training_results)
Sparsity of $h$ against hyperparameter, kernel_regularizer ($\lambda_k$), for training set and testing set
def _sparsity_map(x: int) -> None:
if x != 0:
return 1
else:
return 0
_sparsity_map_vec = np.vectorize(_sparsity_map)
def plot_sparsity(
results,
train_set,
test_set
) -> None:
param = list()
ls_training_sparsity = list()
ls_testing_sparsity = list()
for result in results:
param.append(result['hyperparam'][REGULARIZER_TYPE])
model = result['results']['model']
train_encoded_imgs = model.encoder(train_set).numpy()
test_encoded_imgs = model.encoder(test_set).numpy()
train_sparsity = np.sum(_sparsity_map_vec(train_encoded_imgs))/train_encoded_imgs.size
testing_sparsity = np.sum(_sparsity_map_vec(test_encoded_imgs))/test_encoded_imgs.size
ls_training_sparsity.append(train_sparsity)
ls_testing_sparsity.append(testing_sparsity)
plt.figure(figsize=(12, 8))
plt.plot(param, ls_testing_sparsity, 'bs', label='testing_sparsity')
plt.plot(param, ls_training_sparsity, 'r^', label='training_sparsity')
plt.ylabel('sparsity')
plt.xlabel(REGULARIZER_TYPE)
plt.title('Training sparsity vs testing sparsity')
plt.legend(loc='upper right')
plt.show()
plt.close()
plot_sparsity(
results=training_results,
train_set=x_train_norm,
test_set=x_test_norm,
)
Weight matrix of the encoder, $W_1$, is shown on a grey-scale heatmap. Each of the subplot showing a row frm $W_1$ reshaped to 28x28
def plot_w1(
w1: np.ndarray
) -> None:
w1_dim = int(np.sqrt(len(w1)))
fig, ax = plt.subplots(
nrows=w1_dim,
ncols=w1_dim,
figsize=(w1_dim,w1_dim)
)
plt.gray()
i = 0
for row in ax:
for col in row:
col.imshow(w1[i])
col.get_xaxis().set_visible(False)
col.get_yaxis().set_visible(False)
i = i + 1
plt.show()
plt.close()
for result in training_results:
hyperparam = result['hyperparam']
print(hyperparam)
plot_w1(
w1=result['results']['w1_reshape']
)
{'activity_regularizer': 0.0, 'kernel_regularizer': 0.0}
{'activity_regularizer': 0.0, 'kernel_regularizer': 1.1111111111111112e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 2.2222222222222223e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 3.3333333333333335e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 4.4444444444444447e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 5.555555555555556e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 6.666666666666667e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 7.777777777777778e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 8.888888888888889e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 0.0001}
def plot_images(
img_gp: List[np.ndarray],
num_img: int,
) -> None:
_, ax = plt.subplots(nrows=len(img_gp), ncols=num_img, figsize=(num_img,len(img_gp)))
plt.gray()
for i, row in enumerate(ax):
tmp = img_gp[i]
for j, col in enumerate(row):
col.imshow(tmp[j])
col.get_xaxis().set_visible(False)
col.get_yaxis().set_visible(False)
plt.show()
plt.close()
num_img = 20
img = x_test_norm[:num_img]
for result in training_results:
hyperparam = result['hyperparam']
print(hyperparam)
model = result['results']['model']
encoded_img = model.encoder(img).numpy()
norm_encoded_img = np.divide(encoded_img,np.linalg.norm(encoded_img, axis=1).reshape(-1,1))
decoded_img = model.decoder(encoded_img).numpy()
latent_dim = int(np.sqrt(len(encoded_img.T)))
encoded_img_reshape = encoded_img.reshape((num_img,latent_dim,latent_dim))
norm_encoded_img_reshape = norm_encoded_img.reshape((num_img,latent_dim,latent_dim))
img_gp = [img, encoded_img_reshape, norm_encoded_img_reshape, decoded_img]
plot_images(
img_gp=img_gp,
num_img=num_img,
)
{'activity_regularizer': 0.0, 'kernel_regularizer': 0.0}
{'activity_regularizer': 0.0, 'kernel_regularizer': 1.1111111111111112e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 2.2222222222222223e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 3.3333333333333335e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 4.4444444444444447e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 5.555555555555556e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 6.666666666666667e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 7.777777777777778e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 8.888888888888889e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 0.0001}
def similarity_plot(
img: np.ndarray,
ls_label: List[int]
) -> None:
similarity_matrix = img @ img.T
ls_similarity = [list() for i in range(10)]
ls_disimilarity = [list() for i in range(10)]
for i, u in enumerate(similarity_matrix):
for j, v in enumerate(u):
if i == j:
continue
if ls_label[i] == ls_label[j]:
label = ls_label[i]
ls_similarity[label].append(v)
else:
label = ls_label[i]
ls_disimilarity[label].append(v)
plot_data = [
{
'data': ls_similarity,
'title': 'Cosine similarity of the latent vector with the same label'
},
{
'data': ls_disimilarity,
'title': 'Cosine similarity of the latent vector with the different label',
}
]
_, ax = plt.subplots(nrows=1, ncols=2, figsize=(24,8))
for idx, col in enumerate(ax):
col.boxplot(plot_data[idx]['data'])
col.set_title(plot_data[idx]['title'])
col.set_ylim([0,1])
col.set_xticks(range(1,11))
col.set_xticklabels(range(10))
col.set_xlabel('label')
col.set_ylabel('cosine similarity')
plt.show()
plt.close()
num_img = 1000
img = x_test_norm[:num_img]
img_label = y_test[:num_img]
for result in training_results:
hyperparam = result['hyperparam']
print(hyperparam)
model = result['results']['model']
encoded_img = model.encoder(img).numpy()
norm_encoded_img = np.divide(encoded_img,np.linalg.norm(encoded_img, axis=1).reshape(-1,1))
similarity_plot(img=norm_encoded_img, ls_label=img_label)
{'activity_regularizer': 0.0, 'kernel_regularizer': 0.0}
{'activity_regularizer': 0.0, 'kernel_regularizer': 1.1111111111111112e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 2.2222222222222223e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 3.3333333333333335e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 4.4444444444444447e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 5.555555555555556e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 6.666666666666667e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 7.777777777777778e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 8.888888888888889e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 0.0001}
def tsne_plot(
space_gp: List[np.ndarray],
label: List[int]
) -> None:
_, ax = plt.subplots(nrows=1, ncols=2, figsize=(20,10))
for idx, col in enumerate(ax):
space = space_gp[idx]['space']
scatter = col.scatter(space[:,0], space[:,1], c=label, cmap='Spectral')
col.set_title(space_gp[idx]['title'])
col.set_xlabel('tsne 1')
col.set_ylabel('tsne 2')
col.legend(*scatter.legend_elements())
plt.show()
plt.close()
for result in training_results:
model = result['results']['model']
hyperparam = result['hyperparam']
print(hyperparam)
encoded_img = model.encoder(x_test_norm).numpy()
norm_encoded_img = np.divide(encoded_img,np.linalg.norm(encoded_img, axis=1).reshape(-1,1))
print('fitting tsne for encoded_img')
tsne_space = TSNE(n_components=2, n_jobs=-1).fit_transform(encoded_img)
print('fitting tsne for norm_encoded_img')
tsne_space_norm = TSNE(n_components=2, n_jobs=-1).fit_transform(norm_encoded_img)
space_gp = [
{
'space': tsne_space,
'title': 'Latest space',
},
{
'space': tsne_space_norm,
'title': 'Normalized latest space',
},
]
tsne_plot(space_gp=space_gp, label=y_test)
{'activity_regularizer': 0.0, 'kernel_regularizer': 0.0}
fitting tsne for encoded_img
fitting tsne for norm_encoded_img
{'activity_regularizer': 0.0, 'kernel_regularizer': 1.1111111111111112e-05}
fitting tsne for encoded_img
fitting tsne for norm_encoded_img
{'activity_regularizer': 0.0, 'kernel_regularizer': 2.2222222222222223e-05}
fitting tsne for encoded_img
fitting tsne for norm_encoded_img
{'activity_regularizer': 0.0, 'kernel_regularizer': 3.3333333333333335e-05}
fitting tsne for encoded_img
fitting tsne for norm_encoded_img
{'activity_regularizer': 0.0, 'kernel_regularizer': 4.4444444444444447e-05}
fitting tsne for encoded_img
fitting tsne for norm_encoded_img
{'activity_regularizer': 0.0, 'kernel_regularizer': 5.555555555555556e-05}
fitting tsne for encoded_img
fitting tsne for norm_encoded_img
{'activity_regularizer': 0.0, 'kernel_regularizer': 6.666666666666667e-05}
fitting tsne for encoded_img
fitting tsne for norm_encoded_img
{'activity_regularizer': 0.0, 'kernel_regularizer': 7.777777777777778e-05}
fitting tsne for encoded_img
fitting tsne for norm_encoded_img
{'activity_regularizer': 0.0, 'kernel_regularizer': 8.888888888888889e-05}
fitting tsne for encoded_img
fitting tsne for norm_encoded_img
{'activity_regularizer': 0.0, 'kernel_regularizer': 0.0001}
fitting tsne for encoded_img
fitting tsne for norm_encoded_img
def kmean_plot(
img: np.ndarray,
max_n_cluster: int = 10,
) -> None:
_, ax = plt.subplots(nrows=2, ncols=5, figsize=(25,12))
ax = ax.flatten()
range_clusters = range(2,max_n_cluster+1)
for n_clusters in range_clusters:
kmeans = KMeans(n_clusters=n_clusters)
kmeans.fit(img)
labels = kmeans.labels_
avg_silhouette_score = silhouette_score(img, labels, metric='euclidean')
sample_silhouette_values = silhouette_samples(img, labels)
y_lower = 10
for i in range(n_clusters):
ith_cluster_silhouette_values = sample_silhouette_values[labels == i]
ith_cluster_silhouette_values.sort()
size_cluster_i = ith_cluster_silhouette_values.shape[0]
y_upper = y_lower + size_cluster_i
color = cm.nipy_spectral(float(i) / n_clusters)
ax[n_clusters-1].fill_betweenx(
np.arange(y_lower, y_upper),
0, ith_cluster_silhouette_values,
facecolor=color,
edgecolor=color,
alpha=0.7
)
ax[n_clusters-1].set_xlim([-0.1, 1])
ax[n_clusters-1].set_ylim([0, len(img) + (n_clusters + 1) * 10])
ax[n_clusters-1].text(-0.05, y_lower + 0.5 * size_cluster_i, str(i))
ax[n_clusters-1].set_xlabel('silhouette score')
ax[n_clusters-1].set_ylabel('cluster label')
ax[n_clusters-1].set_title(f'{n_clusters}-clusters')
ax[n_clusters-1].axvline(x=avg_silhouette_score, color="red", linestyle="--")
ax[n_clusters-1].set_xticks([-0.1, 0, 0.2, 0.4, 0.6, 0.8, 1])
ax[n_clusters-1].set_yticks([])
y_lower = y_upper + 10
plt.show()
plt.close()
ls_inertia = list()
for result in training_results:
model = result['results']['model']
hyperparam = result['hyperparam']
print(hyperparam)
encoded_img = model.encoder(x_test_norm).numpy()
norm_encoded_img = np.divide(encoded_img,np.linalg.norm(encoded_img, axis=1).reshape(-1,1))
space_gp = [
{
'space': encoded_img,
'title': 'Latest space',
},
{
'space': norm_encoded_img,
'title': 'Normalized latest space',
},
]
for space in space_gp:
print(f'img = {space["title"]}')
kmean_plot(img=space['space'])
{'activity_regularizer': 0.0, 'kernel_regularizer': 0.0}
img = Latest space
img = Normalized latest space
{'activity_regularizer': 0.0, 'kernel_regularizer': 1.1111111111111112e-05}
img = Latest space
img = Normalized latest space
{'activity_regularizer': 0.0, 'kernel_regularizer': 2.2222222222222223e-05}
img = Latest space
img = Normalized latest space
{'activity_regularizer': 0.0, 'kernel_regularizer': 3.3333333333333335e-05}
img = Latest space
img = Normalized latest space
{'activity_regularizer': 0.0, 'kernel_regularizer': 4.4444444444444447e-05}
img = Latest space
img = Normalized latest space
{'activity_regularizer': 0.0, 'kernel_regularizer': 5.555555555555556e-05}
img = Latest space
img = Normalized latest space
{'activity_regularizer': 0.0, 'kernel_regularizer': 6.666666666666667e-05}
img = Latest space
img = Normalized latest space
{'activity_regularizer': 0.0, 'kernel_regularizer': 7.777777777777778e-05}
img = Latest space
img = Normalized latest space
{'activity_regularizer': 0.0, 'kernel_regularizer': 8.888888888888889e-05}
img = Latest space
img = Normalized latest space
{'activity_regularizer': 0.0, 'kernel_regularizer': 0.0001}
img = Latest space
img = Normalized latest space